Full-dimensional quantum dynamics of SO(X3Σ-) in collision with H2

Quantum rotational dynamics of l-C4(3Σ-g) by H2 at low temperatures employing a machine learning augmented potential energy surface

A new four dimensional (4D) ab initio potential energy surface (PES) is generated for the collision of C4(3Σg-) with H2(1Σg), considering both molecules as rigid rotors. A supervised neural network model is created to augment the ab initio PES and to get the missing data points. Furthermore, space fixed expansion of the augmented PES is carried out using a least squares fit over two spherical harmonics terms, resulting in radial coefficients (λ1, λ2, and λ). The centre of symmetry in both C4 and H2 forces λ1 and λ2 to have even values, respectively. Moreover, the rotational states of C4 are only populated by odd levels due to its ground state triplet symmetry and the nuclear spin (I = 0) of 12C. The cross-sections and rate coefficients with para and ortho H2 partners are studied for various odd state transitions, where the rate coefficients of the ortho are 10-20% higher than those of the latter. The de-excitation rates obtained by the para H2 collisions are also compared to those of He and are found to be ∼1.7-2.8 times the He rates, across various order transitions. The simple scaling of He rates using a factor of 1.38 proves insufficient to describe para H2 rates. Therefore, these results show the importance of explicitly studying H2 as an important colliding partner, governing the kinetics of various rotational processes in the interstellar space.

Pitfalls in the n-mode representation of vibrational potentials

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Vibrational Quenching of Optically Pumped Carbon Dimer Anions

Careful control of quantum states is a gateway to research in many areas of science such as quantum information, quantum-controlled chemistry, and astrophysical processes. Precise optical control of molecular ions remains a challenge due to the scarcity of suitable level schemes, and direct laser cooling has not yet been achieved for either positive or negative molecular ions. Using a cryogenic wire trap, we show how the internal quantum states of C_{2}^{-} anions can be manipulated using optical pumping and inelastic quenching collisions with H_{2} gas. We obtained optical pumping efficiencies of about 96% into the first vibrational level of C_{2}^{-} and determined the absolute inelastic rate coefficient from v=1 to 0 to be k_{q}=(3.2±0.2_{stat}±1.3_{sys})×10^{-13}  cm^{3}/s at 20(3) K, over 3 orders of magnitude smaller than the capture limit. Reduced-dimensional quantum scattering calculations yield a small rate coefficient as well, but significantly larger than the experimental value. Using optical pumping and inelastic collisions, we also realized fluorescence imaging of negative molecular ions. Our work demonstrates high control of a cold ensemble of C_{2}^{-}, providing a solid foundation for future work on laser cooling of molecular ions.

PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials

We wish to describe a potential energy surface by using a basis of permutationally invariant polynomials whose coefficients will be determined by numerical regression so as to smoothly fit a dataset of electronic energies as well as, perhaps, gradients. The polynomials will be powers of transformed internuclear distances, usually either Morse variables, exp(-r_i,j/λ), where λ is a constant range hyperparameter, or reciprocals of the distances, 1/r_i,j. The question we address is how to create the most efficient basis, including (a) which polynomials to keep or discard, (b) how many polynomials will be needed, (c) how to make sure the polynomials correctly reproduce the zero interaction at a large distance, (d) how to ensure special symmetries, and (e) how to calculate gradients efficiently. This article discusses how these questions can be answered by using a set of programs to choose and manipulate the polynomials as well as to write efficient Fortran programs for the calculation of energies and gradients. A user-friendly interface for access to monomial symmetrization approach results is also described. The software for these programs is now publicly available.

Quantum nature of molecular vibrational quenching: Water-molecular hydrogen collisions

Rates of conversions of molecular internal energy to and from kinetic energy by means of molecular collision allow us to compute collisional line shapes and transport properties of gases. Knowledge of ro-vibrational quenching rates is necessary to connect spectral observations to physical properties of warm astrophysical gasses, including exo-atmospheres. For a system of paramount importance in this context, the vibrational bending mode quenching of H₂O by H₂, we show here that the exchange of vibrational to rotational and kinetic energy remains a quantum process, despite the large numbers of quantum levels involved and the large vibrational energy transfer. The excitation of the quantized rotor of the projectile is by far the most effective ro-vibrational quenching path of water. To do so, we use a fully quantum first-principles computation, potential and dynamics, converging it at all stages, in a full coupled channel formalism. We present here rates for the quenching of the first bending mode of ortho-H₂O by ortho-H₂, up to 500 K, in a fully converged coupled channel formalism.

Quantum dynamics of the energy transfer for vibrationally excited HF (v = 7) colliding with D2 (v = 0): Theory assessing experiment

It is still challenging to accurately qualify the rate coefficients for vibrationally excited molecules in experiment. In particular, for the energy transfer between HF (v = 7) and D₂ (v = 0), which is a prototype for near resonant collisional transfer of vibrational excitation from one molecule to the other, the two available experimental results of rate coefficients contradict each other by a factor of nearly 20. In order to benchmark these data, in this work, the rate coefficients of vibration-vibration energy transfer processes of this system at temperatures ranging from 100 to 1500 K were calculated by employing the coupled-states approximation based on our recently developed full-dimensional ab initio intermolecular potential energy surface. The state-to-state rate coefficients were found to follow the general energy gap law. The calculated total vibration-vibration energy transfer rate coefficients decrease with the increase in the angular momentum of HF at most temperatures. The vibrational relaxation rate coefficient decreases monotonously with the temperature, and the calculated result of 8.1 × 10^-11 cm³ mol^-1 s^-1 at room temperature is in very good agreement with the experimental value reported by Dzelzkalns and Kaufman [J. Chem. Phys. 77, 3508 (1982)].

Fine-structure resolved rovibrational transitions for SO + H2 collisions

Cross sections and rate coefficients for sulfur monoxide (SO) + H₂ collisions are calculated using a full six-dimensional (6D) potential energy surface (PES). The coupled states (CS) approximation is used to compute fine-structure resolved cross sections for rovibrational transitions between states with v = 0-2, where v is the vibrational quantum number of the SO molecule. The CS calculations for Δv = 1 are benchmarked against close-coupling (CC) results for spin-free interactions. For Δv = 0, the present fine-structure resolved CS results are benchmarked against existing CC results obtained with a rigid rotor approximation. In both cases, the agreement is found to be satisfactory, which suggests that the present results may provide reliable estimates for fine-structure resolved rovibrational transitions. These estimates are the first of their kind based on a full 6D PES. Rate coefficients are reported for temperatures between 10 K and 3000 K for both para- and ortho-H₂ colliders. A comparison of the para-H₂ rates with mass-scaled results for He shows substantial differences that may be important in astrophysical models.

Evidence of Nonrigidity Effects in the Description of Low-Energy Anisotropic Molecular Collisions of Hydrogen Molecules with Excited Metastable Helium Atoms

Cold collisions serve as a sensitive probe of the interaction potential. In the recent study of Klein et al. (Nature Phys.2017, 13, 35–38), the one-parameter scaling of the interaction potential was necessary to obtain agreement between theoretical and observed patterns of the orbiting resonances for excited metastable helium atoms colliding with hydrogen molecules. Here, we show that the effect of nonrigidity of the H₂ molecule on the resonant structure, absent in the previous study, is critical to predict the correct positions of the resonances in that case. We have complemented the theoretical description of the interaction potential and revised reaction rate coefficients by proper inclusion of the flexibility of the molecule. The calculated reaction rate coefficients are in remarkable agreement with the experimental data without empirical adjustment of the interaction potential. We have shown that even state-of-the-art calculations of the interaction energy cannot ensure agreement with the experiment if such an important physical effect as flexibility of the interacting molecule is neglected. Our findings about the significance of the nonrigidity effects can be especially crucial in cold chemistry, where the quantum nature of molecules is pronounced.